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Time Optimization, Fermat's Principle and Mathematics-Based Technology Enhanced Learning using Excel

Author: Patrick Bruskiewich
Subject: Time Optimization; reflection; refraction; Snell's Law; Fermat's Principle;Mathematics-Based Technology Enhanced Learning; Excel;Carl Wieman Science Education Initiative ; UBC
Language: English
Collection: pythagoraspublishing; additional_collections


We can view reflection of light off a mirror, and refraction of light leading to Snell's Law as a Time Optimization Problem (TOP). Fermat's Principle is that the path traveled by light is the path of least travel time, an explicit description of time optimization. A third TOP problem, flight time between two points, with auxiliary travel constraints, will also be considered in this paper. Solving Time Optimization Problem using a spreadsheet program like EXCEL is a good example of Mathematics-based Technology Enhanced Learning (MTEL) using a widely available software program.

It is more meaningful than lower brain and animation type programs like for instance those used in the Carl Wieman Science Education Initiative at the University of British Columbia.

MTEL is a more meaningful approach merely because animation is a back lobe function, while mathematics and higher reasoning is a frontal lobe one.

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